Final answer:
The correct expression to determine the number of strips of wood that can be cut from 8 2/5 yards of wood, with each strip measuring 7/9 yards, is 8 2/5 ÷ 7/9. The entire calculation is a division problem where the total wood available is divided by the length required for each strip.
Step-by-step explanation:
The goal is to find how many strips of wood a carpenter can cut from a total length of 8 2/5 yards of wood, with each strip requiring 7/9 yards. To figure this out, we need to divide the total length of wood by the length required for each strip. The correct mathematical operation for this is division, and the corresponding expression is 8 2/5 ÷ 7/9.
Expression (d) 4 2/5 ÷ 7/9 actually has a typo and should have been 8 2/5 ÷ 7/9. This expression represents the total yards of wood available divided by the yards needed per strip. By using this expression, the carpenter can calculate the exact number of strips that can be cut from the total wood length. The other options either use incorrect mathematical operations or have numbers that do not match the given quantities.
Option (e) 8 2/5 × 7/9 represents multiplying the total wood length by the length per strip, which is not the correct operation for finding the number of strips. Option (a) 7/9 × 4 2/5 uses incorrect numbers, and option (b) 4 2/5 × 9/7 represents an inverse operation that isn't applicable to this problem. Finally, option (c) 7/9 ÷ 5 4/2 includes an irrelevant fraction and is not the right expression to use.